THE father of two young children who were killed by their nanny has described the harrowing moment he learned of their deaths just after his plane landed and how he said goodbye to them.

Kevin Krim told jurors in the trial of nanny Yoselyn Ortega that when he switched off the aeroplane mode function on his mobile phone at John F. Kennedy International Airport in New York he was flooded with text messages from concerned neighbours and friends.

He said he was trying to figure it out and "fumbling around" when a flight attendant asked him to go to the cockpit.

"It's the worst thing imaginable. I was hoping it was a nightmare, and it wasn't," said Mr Krim, recalling that he sat down in the galley after getting a call from his father-in-law.

Yoselyn Ortega, centre, charged with the stabbing deaths of two small children under her care, is escorted to her seat for her first court appearance in New York. Picture: AP

He said two plainclothes police officers had to pick him up off the floor, somebody grabbed him by the arm and somebody grabbed his bag. He said he kept asking "What's going on?" and then saw there was a voicemail from his wife, Marina Krim.

"I pressed play to listen to it, and I just heard the background noise of screaming," he testified. "I crumbled to the ground."

"She rushed up to me and hugged me, and then she pushed me away, and said, 'We're not gonna get divorced, people always get divorced when things happen to their kids. Oprah says people always get divorced when they lose kids. We're not gonna get divorced.' I don't think I said anything, I was in shock," he said.

Photographs of six-year-old Lucia Krim and her two-year-old brother, Leo, are displayed alongside balloons and stuffed animals at a memorial outside the apartment building where they lived in New York. Picture: AP

Mr Krim said that his children, Lulu and Leo were lying on hospital tables, with sheets up to their chins.

"They looked beautiful and strange. They had lost a lot of blood, so they were blue. But they still had this perfect skin, the long eye lashes,' Mr Krim said. "They'd had this, like, sandy brown hair, and you see [the doctors] had tried really hard to wash all the blood out, but there was still kind of an auburn tint to it that I remember to this day."

"I got down on my knees, and I said, 'I'm sorry.' I said, 'I love you,' and I kissed them, and I said goodbye," Mr Krim said.

The building where two children were stabbed to death allegedly by their nanny in a family's Upper West Side apartment. Picture: Getty

Ms Ortega has pleaded not guilty in the fatal stabbings of two-year-old Leo Krim and six-year-old Lucia Krim, known as Lulu, in October 2012.

Her lawyers don't dispute that she killed the children but say she's too mentally ill to be responsible for what she did.